Find the zeros of the function. Enter the solutions from least to greatest. $f(x)=(x-5)(5x+2)$ $\text{lesser }x = $
Answer: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(x-5)(5x+2)=0$. So either $x-5=0$ or $5x+2=0$ : $\begin{aligned} (1)&&x-5&=0 \\\\ &&x&=5 \end{aligned}$ $\begin{aligned} (2)&&5x+2&=0 \\\\ &&5x&=-2 \\\\ &&x&=-\dfrac25 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -\dfrac25 \\\\ \text{greater } x &= 5 \end{aligned}$